Meghann Shaughnessy, standing in for the world number seven, gave the US a perfect start to the warm-up event for next month's Australian Open by beating Sania Mirza 6-3, 4-6, 6-3.
Mardy Fish sealed the win with a 6-2, 6-4 victory over Rohan Bopanna before the Indian pair took the doubles 6-4, 6-4.
Williams is due to arrive in Perth in time for her nation's second group match in the eight-nation mixed-team tournament against the Czech Republic on Monday.
World number 52 Shaughnessy won the first four games against an erratic Mirza and looked on course for a quick win when she led by a set and 2-0.
However, Mirza hit back to level and then took command at 3-1 in the decider only to falter when it mattered, losing the last five games to hand Shaughnessy the win. "I got the call a couple of days ago," said Shaughnessy, who left within minutes of the doubles to catch a flight to Australia's Gold Coast, where she is due to play in the WTA event starting on Sunday.
"I sort of feel like I've got a couple of matches under my belt already, just from that one match. It's great preparation." Fish then breezed past world number 267 Bopanna, easing to victory in one hour, 12 minutes to render the mixed doubles a dead rubber.
"I'm extremely pleased," Fish said in a courtside interview. "Rohan's a very dangerous player and you never know what to expect after the off-season but it was very good."
Later, Alicia Molik inspired hosts Australia to a 2-1 win over third seeds Czech Republic. Home favourite Molik made an excellent start beating Lucie Safarova 7-5, 6-2 to put Australia ahead in their Group A match. The 27-year-old won four straight games from 5-5 to take the first set and lead 2-0 in the second. The Australian hit 13 aces and world number 23 Safarova had no answer as Molik eased through the second set for victory.
World number 79 Peter Luczak had a set point in the opening-set tiebreak before going down 7-6, 6-4 to Tomas Berdych, ranked 65 places above him. But the 18-year-old Luczak then joined with Molik to beat the boyfriend-girlfriend pairing of Berdych and Safarova 7-5 6-3.
Slow surface
World number three Novak Djokovic and other top players have said that the new Plexicushion surface that will be used at next month's Australian Open is slower than they had expected. After 20 years of using Rebound Ace, Australian Open organisers made the change in an effort to make all the courts t more consistent in terms of speed and bounce.